Pairing around a Single Dirac Point: Superconductivity from Repulsion Requires Broken Time-Reversal
Author: Scaffidi, Thomas
Affiliation: UC Irvine
Type: Contributed Talk
Session: Topological superconductivity in Weyl systems
Date and Time: 22.07.2026, 12:35 - 12:55
Recent experimental discoveries of superconductivity in valley-polarized systems, such as the quarter-metal phase of rhombohedral graphene, have challenged traditional paradigms of electron pairing. Concurrently, a wave of new theoretical work—including recent studies on the doped Hofstadter model—has revealed that systems with broken time-reversal symmetry (TRS) in the normal state are surprisingly promising platforms for unconventional superconductivity. Motivated by these developments, this talk explores the conditions under which a single, two-dimensional doped Dirac cone can spontaneously develop intrinsic superconductivity from purely repulsive interactions via the Kohn-Luttinger (weak-coupling) mechanism. We will first establish a striking dichotomy: an ideal, purely linear Dirac cone is completely immune to pairing at leading order in the interaction. However, superconductivity is robustly restored by higher-order momentum corrections to the dispersion. These terms, which are inevitable in any lattice realization, are not merely minor corrections but the fundamental drivers that dictate the pairing symmetry. We highlight two main pathways that allow this superconductivity to emerge. First, if the Dirac cone arises from broken time-reversal symmetry, the system stabilizes into a fully gapped, topological p-ip superconducting state with a chirality opposite to that of the parent metal. Second, if time-reversal symmetry is preserved, e.g. at the surface of a 3D topological insulator, the pairing is instead driven by the anisotropy of the band structure, leading to complex but nodal superconducting gaps.